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№1 слайд![Translational Equilibrium](/documents_6/df3d77322f0173e89150bd89af7ab086/img0.jpg)
Содержание слайда: Translational Equilibrium
№2 слайд![Objectives Describe with](/documents_6/df3d77322f0173e89150bd89af7ab086/img1.jpg)
Содержание слайда: Objectives
Describe with examples Newton’s three laws of motion.
Describe with examples the first condition for equilibrium.
Draw free-body diagrams for objects in translational equilibrium.
Apply the first condition for equilibrium to the solution of problems.
№3 слайд![Newton s First Law Newton s](/documents_6/df3d77322f0173e89150bd89af7ab086/img2.jpg)
Содержание слайда: Newton’s First Law
Newton’s First Law: An object at rest or an object in motion at constant speed will remain at rest or at constant speed in the absence of a resultant force.
№4 слайд![Newton s Second Law Second](/documents_6/df3d77322f0173e89150bd89af7ab086/img3.jpg)
Содержание слайда: Newton’s Second Law:
Second Law: Whenever a resultant force acts on an object, it produces an acceleration - an acceleration that is directly proportional to the force and inversely proportional to the mass.
№5 слайд![Newton s Third Law To every](/documents_6/df3d77322f0173e89150bd89af7ab086/img4.jpg)
Содержание слайда: Newton’s Third Law
To every action force there must be an equal and opposite reaction force.
№6 слайд![Newton s Third Law Examples](/documents_6/df3d77322f0173e89150bd89af7ab086/img5.jpg)
Содержание слайда: Newton’s Third Law
Examples:
№7 слайд![Translational Equilibrium An](/documents_6/df3d77322f0173e89150bd89af7ab086/img6.jpg)
Содержание слайда: Translational Equilibrium
An object is said to be in Translational Equilibrium if and only if there is no resultant force.
This means that the sum of all acting forces is zero.
№8 слайд![Visualization of Forces](/documents_6/df3d77322f0173e89150bd89af7ab086/img7.jpg)
Содержание слайда: Visualization of Forces
№9 слайд![Visualization of Forces](/documents_6/df3d77322f0173e89150bd89af7ab086/img8.jpg)
Содержание слайда: Visualization of Forces
№10 слайд![Vector Sum of Forces An](/documents_6/df3d77322f0173e89150bd89af7ab086/img9.jpg)
Содержание слайда: Vector Sum of Forces
An object is said to be in Translational Equilibrium if and only if there is no resultant force.
The vector sum of all forces acting on the ring is zero in this case.
№11 слайд![Vector Force Diagram](/documents_6/df3d77322f0173e89150bd89af7ab086/img10.jpg)
Содержание слайда: Vector Force Diagram
№12 слайд![Look Again at Previous](/documents_6/df3d77322f0173e89150bd89af7ab086/img11.jpg)
Содержание слайда: Look Again at Previous Arrangement
№13 слайд![Translational Equilibrium The](/documents_6/df3d77322f0173e89150bd89af7ab086/img12.jpg)
Содержание слайда: Translational Equilibrium
The First Condition for Equilibrium is that there be no resultant force.
This means that the sum of all acting forces is zero.
№14 слайд![Example . Find the tensions](/documents_6/df3d77322f0173e89150bd89af7ab086/img13.jpg)
Содержание слайда: Example 2. Find the tensions in ropes A and B for the arrangement shown.
№15 слайд![Example . Continued . . .](/documents_6/df3d77322f0173e89150bd89af7ab086/img14.jpg)
Содержание слайда: Example 2. Continued . . .
№16 слайд![Example . Continued . . .](/documents_6/df3d77322f0173e89150bd89af7ab086/img15.jpg)
Содержание слайда: Example 2. Continued . . .
№17 слайд![Example . Continued . . .](/documents_6/df3d77322f0173e89150bd89af7ab086/img16.jpg)
Содержание слайда: Example 2. Continued . . .
№18 слайд![Problem Solving Strategy](/documents_6/df3d77322f0173e89150bd89af7ab086/img17.jpg)
Содержание слайда: Problem Solving Strategy
№19 слайд![Example . Find Tension in](/documents_6/df3d77322f0173e89150bd89af7ab086/img18.jpg)
Содержание слайда: Example 3. Find Tension in Ropes A and B.
№20 слайд![Example . Find the tension in](/documents_6/df3d77322f0173e89150bd89af7ab086/img19.jpg)
Содержание слайда: Example 3. Find the tension in ropes A and B.
№21 слайд![Example . Find the tension in](/documents_6/df3d77322f0173e89150bd89af7ab086/img20.jpg)
Содержание слайда: Example 3. Find the tension in ropes A and B.
№22 слайд![Example Cont. Find the](/documents_6/df3d77322f0173e89150bd89af7ab086/img21.jpg)
Содержание слайда: Example 3 (Cont.) Find the tension in A and B.
№23 слайд![Example Cont. Find Tensions](/documents_6/df3d77322f0173e89150bd89af7ab086/img22.jpg)
Содержание слайда: Example 3 (Cont.) Find Tensions in A and B.
№24 слайд![Example Cont. Find B with A N.](/documents_6/df3d77322f0173e89150bd89af7ab086/img23.jpg)
Содержание слайда: Example 3 (Cont.) Find B with A = 200 N.
№25 слайд![Example . Rotate axes for](/documents_6/df3d77322f0173e89150bd89af7ab086/img24.jpg)
Содержание слайда: Example 4. Rotate axes for same example.
№26 слайд![Since A and B are](/documents_6/df3d77322f0173e89150bd89af7ab086/img25.jpg)
Содержание слайда: Since A and B are perpendicular, we can find the new angle from geometry.
№27 слайд![](/documents_6/df3d77322f0173e89150bd89af7ab086/img26.jpg)
№28 слайд![Example Cont. We Now Solve](/documents_6/df3d77322f0173e89150bd89af7ab086/img27.jpg)
Содержание слайда: Example 4 (Cont.) We Now Solve for A and B:
№29 слайд![](/documents_6/df3d77322f0173e89150bd89af7ab086/img28.jpg)
№30 слайд![](/documents_6/df3d77322f0173e89150bd89af7ab086/img29.jpg)
№31 слайд![](/documents_6/df3d77322f0173e89150bd89af7ab086/img30.jpg)
№32 слайд![](/documents_6/df3d77322f0173e89150bd89af7ab086/img31.jpg)
№33 слайд![Summary Newton s First Law An](/documents_6/df3d77322f0173e89150bd89af7ab086/img32.jpg)
Содержание слайда: Summary
Newton’s First Law: An object at rest or an object in motion at constant speed will remain at rest or at constant speed in the absence of a resultant force.
№34 слайд![Summary Second Law Whenever a](/documents_6/df3d77322f0173e89150bd89af7ab086/img33.jpg)
Содержание слайда: Summary
Second Law: Whenever a resultant force acts on an object, it produces an acceleration, an acceleration that is directly proportional to the force and inversely proportional to the mass.
№35 слайд![Summary Third Law To every](/documents_6/df3d77322f0173e89150bd89af7ab086/img34.jpg)
Содержание слайда: Summary
Third Law: To every action force there must be an equal and opposite reaction force.
№36 слайд![Problem Solving Strategy](/documents_6/df3d77322f0173e89150bd89af7ab086/img35.jpg)
Содержание слайда: Problem Solving Strategy
№37 слайд![Friction and Equilibrium](/documents_6/df3d77322f0173e89150bd89af7ab086/img36.jpg)
Содержание слайда: Friction and Equilibrium
№38 слайд![Objectives Define and](/documents_6/df3d77322f0173e89150bd89af7ab086/img37.jpg)
Содержание слайда: Objectives
Define and calculate the coefficients of kinetic and static friction, and give the relationship of friction to the normal force.
Apply the concepts of static and kinetic friction to problems involving constant motion or impending motion.
№39 слайд![Friction Forces](/documents_6/df3d77322f0173e89150bd89af7ab086/img38.jpg)
Содержание слайда: Friction Forces
№40 слайд![Friction and the Normal Force](/documents_6/df3d77322f0173e89150bd89af7ab086/img39.jpg)
Содержание слайда: Friction and the Normal Force
№41 слайд![Friction forces are](/documents_6/df3d77322f0173e89150bd89af7ab086/img40.jpg)
Содержание слайда: Friction forces are independent of area.
№42 слайд![Friction forces are](/documents_6/df3d77322f0173e89150bd89af7ab086/img41.jpg)
Содержание слайда: Friction forces are independent of speed.
№43 слайд![The Static Friction Force](/documents_6/df3d77322f0173e89150bd89af7ab086/img42.jpg)
Содержание слайда: The Static Friction Force
№44 слайд![Constant or Impending Motion](/documents_6/df3d77322f0173e89150bd89af7ab086/img43.jpg)
Содержание слайда: Constant or Impending Motion
№45 слайд![Friction and Acceleration](/documents_6/df3d77322f0173e89150bd89af7ab086/img44.jpg)
Содержание слайда: Friction and Acceleration
№46 слайд![EXAMPLE If k . and s . , what](/documents_6/df3d77322f0173e89150bd89af7ab086/img45.jpg)
Содержание слайда: EXAMPLE 1: If k = 0.3 and s = 0.5, what horizontal pull P is required to just start a 250-N block moving?
№47 слайд![EXAMPLE Cont. s . , W N. Find](/documents_6/df3d77322f0173e89150bd89af7ab086/img46.jpg)
Содержание слайда: EXAMPLE 1(Cont.): s = 0.5, W = 250 N. Find P to overcome fs (max). Static friction applies.
№48 слайд![EXAMPLE Cont. s . , W N. Find](/documents_6/df3d77322f0173e89150bd89af7ab086/img47.jpg)
Содержание слайда: EXAMPLE 1(Cont.): s = 0.5, W = 250 N. Find P to overcome fs (max). Now we know n = 250 N.
№49 слайд![EXAMPLE Cont. If k . and s .](/documents_6/df3d77322f0173e89150bd89af7ab086/img48.jpg)
Содержание слайда: EXAMPLE 1(Cont.): If k = 0.3 and s = 0.5, what horizontal pull P is required to move with constant speed? (Overcoming kinetic friction)
№50 слайд![The Normal Force and Weight](/documents_6/df3d77322f0173e89150bd89af7ab086/img49.jpg)
Содержание слайда: The Normal Force and Weight
№51 слайд![For Friction in Equilibrium](/documents_6/df3d77322f0173e89150bd89af7ab086/img50.jpg)
Содержание слайда: For Friction in Equilibrium:
Draw free-body diagram for each body.
Choose x or y-axis along motion or impending motion and choose direction of motion as positive.
Identify the normal force and write one of following:
fs = sn or fk = kn
For equilibrium, we write for each axis:
Fx = 0 Fy = 0
Solve for unknown quantities.
№52 слайд![Example . A force of N drags](/documents_6/df3d77322f0173e89150bd89af7ab086/img51.jpg)
Содержание слайда: Example 2. A force of 60 N drags a 300-N block by a rope at an angle of 400 above the horizontal surface. If uk = 0.2, what force P will produce constant speed?
№53 слайд![Example Cont. . P ? W N uk . .](/documents_6/df3d77322f0173e89150bd89af7ab086/img52.jpg)
Содержание слайда: Example 2 (Cont.). P = ?; W = 300 N; uk = 0.2.
№54 слайд![Example Cont. . P ? W N uk . .](/documents_6/df3d77322f0173e89150bd89af7ab086/img53.jpg)
Содержание слайда: Example 2 (Cont.). P = ?; W = 300 N; uk = 0.2.
№55 слайд![Example Cont. . P ? W N uk . .](/documents_6/df3d77322f0173e89150bd89af7ab086/img54.jpg)
Содержание слайда: Example 2 (Cont.). P = ?; W = 300 N; uk = 0.2.
№56 слайд![Example Cont. . P ? W N uk . .](/documents_6/df3d77322f0173e89150bd89af7ab086/img55.jpg)
Содержание слайда: Example 2 (Cont.). P = ?; W = 300 N; uk = 0.2.
№57 слайд![Example What push P up the](/documents_6/df3d77322f0173e89150bd89af7ab086/img56.jpg)
Содержание слайда: Example 3: What push P up the incline is needed to move a 230-N block up the incline at constant speed if k = 0.3?
№58 слайд![Example Cont. Find P to give](/documents_6/df3d77322f0173e89150bd89af7ab086/img57.jpg)
Содержание слайда: Example 3 (Cont.): Find P to give move up the incline (W = 230 N).
№59 слайд![Summary](/documents_6/df3d77322f0173e89150bd89af7ab086/img58.jpg)
Содержание слайда: Summary
№60 слайд![Summary Important Points Cont.](/documents_6/df3d77322f0173e89150bd89af7ab086/img59.jpg)
Содержание слайда: Summary: Important Points (Cont.)
№61 слайд![Summary Important Points Cont.](/documents_6/df3d77322f0173e89150bd89af7ab086/img60.jpg)
Содержание слайда: Summary: Important Points (Cont.)
№62 слайд![Summary](/documents_6/df3d77322f0173e89150bd89af7ab086/img61.jpg)
Содержание слайда: Summary
№63 слайд![Summary](/documents_6/df3d77322f0173e89150bd89af7ab086/img62.jpg)
Содержание слайда: Summary